Substrate effects on spin relaxation in two-dimensional Dirac materials with strong spin-orbit coupling

Abstract Understanding substrate effects on spin dynamics and relaxation is of key importance for spin-based information technologies. However, the key factors that determine such effects, in particular for materials with strong spin-orbit coupling (SOC), have not been well understood. Here we performed first-principles real-time density-matrix dynamics simulations with SOC and the electron-phonon and electron-impurity scattering for spin lifetimes ( τ s ) of supported/free-standing germanene, a prototypical strong SOC 2D Dirac material. We show that the effects of different substrates on τ s can surprisingly differ by two orders of magnitude. We find that substrate effects on τ s are closely related to substrate-induced modifications of the SOC-field anisotropy, which changes the spin-flip scattering matrix elements. We propose a new electronic quantity, named spin-flip angle θ ↑ ↓ , to characterize spin relaxation through intervalley spin-flip scattering. We find that $${\tau }_{s}^{-1}$$ τ s − 1 is approximately proportional to the averaged value of $${\sin }^{2}\left({\theta }^{\uparrow \downarrow }/2\right)$$ sin 2 θ ↑ ↓ / 2 , which serves as a guiding parameter of controlling spin relaxation.